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Properties

Label 255.2.a
Level $255$
Weight $2$
Character orbit 255.a
Rep. character $\chi_{255}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $4$
Sturm bound $72$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 255 = 3 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 255.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(72\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(255))\).

Total New Old
Modular forms 40 11 29
Cusp forms 33 11 22
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(5\)\(17\)FrickeDim
\(+\)\(+\)\(-\)$-$\(2\)
\(+\)\(-\)\(+\)$-$\(2\)
\(-\)\(+\)\(+\)$-$\(4\)
\(-\)\(-\)\(-\)$-$\(3\)
Plus space\(+\)\(0\)
Minus space\(-\)\(11\)

Trace form

\( 11 q + 5 q^{2} + 3 q^{3} + 17 q^{4} - q^{5} - 3 q^{6} + 8 q^{7} + 9 q^{8} + 11 q^{9} + O(q^{10}) \) \( 11 q + 5 q^{2} + 3 q^{3} + 17 q^{4} - q^{5} - 3 q^{6} + 8 q^{7} + 9 q^{8} + 11 q^{9} + q^{10} + 12 q^{11} + 5 q^{12} + 2 q^{13} - 8 q^{14} - q^{15} + 17 q^{16} - q^{17} + 5 q^{18} - 4 q^{19} - 7 q^{20} + 8 q^{21} - 12 q^{22} + 8 q^{23} - 15 q^{24} + 11 q^{25} - 18 q^{26} + 3 q^{27} - 8 q^{28} + 2 q^{29} - 3 q^{30} - 8 q^{31} - 7 q^{32} - 12 q^{33} - 3 q^{34} + 17 q^{36} + 26 q^{37} - 28 q^{38} + 2 q^{39} - 3 q^{40} + 6 q^{41} - 24 q^{42} - 4 q^{43} - 12 q^{44} - q^{45} - 32 q^{46} - 16 q^{47} - 3 q^{48} + 27 q^{49} + 5 q^{50} - q^{51} - 58 q^{52} + 10 q^{53} - 3 q^{54} - 12 q^{55} - 72 q^{56} + 28 q^{57} - 34 q^{58} - 20 q^{59} - 7 q^{60} - 14 q^{61} - 64 q^{62} + 8 q^{63} - 19 q^{64} + 18 q^{65} - 8 q^{66} - 4 q^{67} - 7 q^{68} - 16 q^{69} - 12 q^{70} + 9 q^{72} + 38 q^{73} - 10 q^{74} + 3 q^{75} - 8 q^{76} + 6 q^{78} - 16 q^{79} + q^{80} + 11 q^{81} - 6 q^{82} - 4 q^{83} - 4 q^{84} + 3 q^{85} + 44 q^{86} - 6 q^{87} - 12 q^{88} + 38 q^{89} + q^{90} - 8 q^{91} + 56 q^{92} + 24 q^{93} + 20 q^{94} - 20 q^{95} - 23 q^{96} + 30 q^{97} + 61 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(255))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 17
255.2.a.a 255.a 1.a $2$ $2.036$ \(\Q(\sqrt{13}) \) None \(1\) \(-2\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
255.2.a.b 255.a 1.a $2$ $2.036$ \(\Q(\sqrt{5}) \) None \(3\) \(-2\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
255.2.a.c 255.a 1.a $3$ $2.036$ 3.3.229.1 None \(0\) \(3\) \(3\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
255.2.a.d 255.a 1.a $4$ $2.036$ 4.4.13768.1 None \(1\) \(4\) \(-4\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+q^{3}+(2-\beta _{1})q^{4}-q^{5}-\beta _{3}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(255))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(255)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 2}\)